Late-Time Tail of Wave Propagation on Curved Spacetime

Ching, Emily S. C.; Leung, P. T.; Suen, Wai-Mo; Young, K.

doi:10.1103/physrevlett.74.2414

Cited by 127 publications

(223 citation statements)

References 12 publications

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“…(7.4) would start at k = 1 2 (l − m) − 1 and we would have 6) in agreement with the generic results displayed in Table I. We see that reconciliation between the results of Sec.…”

Section: Direct Comparison Between Spheroidal and Spherical Descsupporting

confidence: 80%

“…The work of Ching et al [6] is especially noteworthy, because it contributes a very simple heuristic understanding of the inverse power-law decay. These authors show that the late-time field at the spatial position r is produced by the part of the initial wave packet that propagates outward to a distant point r ′′ (such that r ′′ is much larger than r), scatters off a small amount of spacetime curvature there, and makes its way back to r after a time t ≃ 2r ′′ .…”

Section: Radiative Falloff In Spherical Spacetimesmentioning

confidence: 99%

“…After multiplying the field by r to produce a nonzero result, we find 6) up to a fractional correction of order L 2 /u 2 . These results agree precisely with those obtained previously for Schwarzschild spacetime [3,5].…”

Section: Radiative Falloff In Spherical Spacetimesmentioning

confidence: 99%

“…Making repeated use of the binomial theorem, we re-express the Green's function as 6) where S ≡ sin θ sin θ ′ cos(φ − φ ′ ) and C ≡ cos θ ′ . After substituting this into Eq.…”

Section: Radiative Falloff In Spheroidal Coordinatesmentioning

confidence: 99%

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Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Poisson

2002

Phys. Rev. D

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We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.

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“…(7.4) would start at k = 1 2 (l − m) − 1 and we would have 6) in agreement with the generic results displayed in Table I. We see that reconciliation between the results of Sec.…”

Section: Direct Comparison Between Spheroidal and Spherical Descsupporting

confidence: 80%

Section: Radiative Falloff In Spherical Spacetimesmentioning

confidence: 99%

Section: Radiative Falloff In Spherical Spacetimesmentioning

confidence: 99%

Section: Radiative Falloff In Spheroidal Coordinatesmentioning

confidence: 99%

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Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Poisson

2002

Phys. Rev. D

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“…In cases where the φ j 's are not complete, it may still be possible to characterize the remainder, which could be, for example, a power law in t for long times [20,21]. Moreover, when the eigenstates are complete, one can set up a formalism that closely parallels the conservative case (see Refs.…”

Section: B Quasinormal Modesmentioning

confidence: 99%

SUSY transformations for quasinormal modes of open systems

Leung

Brink

Suen

et al. 2001

Journal of Mathematical Physics

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Supersymmetry (SUSY) in quantum mechanics is extended from square-integrable states to those satisfying the outgoing-wave boundary condition, in a Klein-Gordon formulation. This boundary condition allows both the usual normal modes and quasinormal modes with complex eigenvalues ω. The simple generalization leads to three features: the counting of eigenstates under SUSY becomes more systematic; the linear-space structure of outgoing waves (nontrivially different from the usual Hilbert space of square-integrable states) is preserved by SUSY; and multiple states at the same frequency (not allowed for normal modes) are also preserved. The existence or otherwise of SUSY partners is furthermore relevant to the question of inversion: are open systems uniquely determined by their complex outgoing-wave spectra?

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Green's Function Approach for Late‐Time Tail and Echoes in Damour–Solodukhin Type Wormholes

Qian,

Pan,

et al. 2024

Astron Nachr

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This study elaborates on two distinctive features in Damour–Solodukhin wormhole's waveforms: late‐time tails and echoes. As a well‐known black hole mimicker, these characteristics are crucial in differentiating wormholes from classical black holes. They emerge in the final phases of quasinormal oscillations and arise from specific structures in the Green's function. The late‐time tail results from branch cut contributions, indicating a need to refine our interpretation of spacetime geometry. The echoes originate from additional quasinormal modes, similar to scenarios with metric discontinuities. These observations suggest that late‐time wave behavior could be a unique signature of wormholes. Furthermore, the study hints at a possible interaction between late‐time tails and echoes in the waveform's evolution.

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Late-Time Tail of Wave Propagation on Curved Spacetime

Cited by 127 publications

References 12 publications

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

SUSY transformations for quasinormal modes of open systems

Green's Function Approach for Late‐Time Tail and Echoes in Damour–Solodukhin Type Wormholes

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